Wash the leeks thoroughly to remove any dirt and transfer to a large bowl. Add the carrots, chickpeas and 2 tablespoons of the herbes de Provence. Drizzle with olive oil and season with salt and pepper. Stir well to combine. Transfer to a rimmed baking sheet.
To spatchcock the chicken, use strong kitchen shears or poultry shears and cut down both sides of the backbone. Pull out the backbone, turn the chicken over and press down on the breast to flatten it out to one thickness.
Place the chicken on top of the vegetables in the baking sheet. Drizzle the chicken with olive oil and season with salt, pepper and the remaining 1 tablespoon herbes de Provence.
Roast in the oven until the chicken skin is golden brown and crisp and a thermometer inserted into a thigh registers 165 degrees F, 45 to 55 minutes.
Transfer the chicken to a cutting board and let rest for 10 minutes. Transfer the roasted vegetables to a large saute pan and add the spinach and mustard. Stir to combine, letting the residual heat from the vegetables wilt the spinach. If desired, cook the spinach further on the stovetop.